On return-volatility correlation in financial dynamics

TL;DR

This paper investigates the origin of return-volatility correlation in financial markets using data from German DAX and Chinese indices, proposing a model that isolates the feedback interactions responsible for this correlation.

Contribution

It introduces a retarded volatility model that can eliminate or generate return-volatility correlation without affecting other statistical properties of the data.

Findings

Return-volatility correlation arises from feedback return-volatility interactions.

Large volatilities significantly influence the return-volatility correlation.

Long-range volatility correlations are not the primary cause of the correlation.

Abstract

With the daily and minutely data of the German DAX and Chinese indices, we investigate how the return-volatility correlation originates in financial dynamics. Based on a retarded volatility model, we may eliminate or generate the return-volatility correlation of the time series, while other characteristics, such as the probability distribution of returns and long-range time-correlation of volatilities etc., remain essentially unchanged. This suggests that the leverage effect or anti-leverage effect in financial markets arises from a kind of feedback return-volatility interactions, rather than the long-range time-correlation of volatilities and asymmetric probability distribution of returns. Further, we show that large volatilities dominate the return-volatility correlation in financial dynamics.